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arXiv:quant-ph/0204164 · Physical Review A

Berry’s phase in cavity QED: Proposal for observing an effect of field quantization

Angelo C. M. Carollo, Marcelo França Santos, Vlatko Vedral

Published Jun 16, 2003• 37 citations
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Abstract

We propose a feasible experiment to investigate quantum effects in geometric phases, arising when a classical source drives not a single quantum system, but two interacting ones. In particular, we show how to observe a signature of the quantization of the electromagnetic field through a vacuum effect in Berry's phase. To do so, we describe the interaction of an atom and a quantized cavity mode altogether driven by an external quasiclassical field. We also analyze the semiclassical limit recovering the usual Berry's phase results.

DOI
10.1103/physreva.67.063804

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We propose a feasible experiment to investigate quantum effects in geometric phases, arising when a classical source drives not a single quantum system, but two interacting ones. In particular, we show how to observe a signature of the quantization of the electromagnetic field through a vacuum effect in Berry's phase. To do so, we describe the interaction of an atom and a quantized cavity mode altogether driven by an external quasiclassical field. We also analyze the semiclassical limit recovering the usual Berry's phase results.
Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Berry phases for the whole system and subsystem are studied. The effect of couplings between particles and photon on these phases are analyzed. In comparison with the dynamical quantized field, We find that even a static quantized field in its vacuum state can also have an effect on Berry phase. Second, quantized field driven Berry phases for the whole system and sub- system are formulated, including both one and two mode of this field. The vacuum induced effects are elaborated, moreover compared with the constant vacuum induced phases in former papers, the counterpart in this letter varies according to classical magnetic field, couplings and other pa- rameters. For the two mode quantized field, the rigorous relationship between the concurrence and Berry phase for subsystem are built up.
Motivated by work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquired photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even if the field is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with a cavity quantum electrodynamics system is designed to detect the vacuum-induced Berry phase.
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing.
Since a pioneer work on vacuum-induced Berry phase (VIBP) was done by Fuentes-Guridi et al. [Phys. Rev. Lett. 89 (2002) 220404], much attention has been paid to the geometric phase effects of vacuum field. However, all the so-called VIBPs investigated previously are not purely vacuum-induced (i.e. the nonvacuum components of the field are also involved). In this paper, we discuss how to deliver geometric phases from the evolution of a genuine vacuum field in a standard cavity quantum electrodynamics (QED) system. First, we design a cyclic evolution of an atom–field system with the atom being initially prepared at the excited state and the field at the genuine vacuum. Then, we calculate the geometric phases acquired during such a cyclic evolution. It is found that such geometric phases are really induced by an evolution of the genuine vacuum field. Specifically, our generic proposal is demonstrated with both the one- and two-mode Jaynes–Cummings model interactions (JCM).
The effect of intersubsystem coupling on the Berry phase of a composite system as well as that of its subsystem is investigated. We analyze two coupled spin-12\frac{1}{2}21​ systems with one driven by a quantized field as an example. The pure-state geometric phase of the composite system as well as the mixed-state geometric phase for the subsystem is calculated and discussed.